Problem: Simplify the following expression: $\sqrt{54} + \sqrt{6}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{54} + \sqrt{6}$ $= \sqrt{9 \cdot 6} + \sqrt{6}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{6} + \sqrt{6}$ $= 3\sqrt{6} + \sqrt{6}$ Finally, simplify by combining the terms. $= ( 3 + 1 )\sqrt{6} = 4\sqrt{6}$